Guest Speaker

Anisotropic Triangulations

Jonathan Richard Shewchuk
http://www.cs.berkeley.edu/~jrs/
Computer Science Division
University of California at Berkeley

Thursday, November 6th
3:30 p.m.; 480 Dreese Labs
All interested parties are invited.
Refreshments will be served immediately preceding the talk.

Abstract:
For applications in graphics and scientific computing, anisotropic meshes often
offer the best tradeoff between accuracy and size. Long, thin triangles or
tetrahedra are appropriate for interpolating functions with anisotropic
curvature, and for approximating solutions to anisotropic partial differential
equations.

The first part of this talk summarizes the connections between interpolation
errors, stiffness matrix conditioning, and the shapes of triangles or
tetrahedra. This background explains how to tell what aspect ratio and
orientation an ideal triangle or tetrahedron should have, to best fit the needs
of an application. The second part of this talk introduces {\em anisotropic
Voronoi diagrams}, which are suitable for generating guaranteed-quality
anisotropic meshes wherein the desired anisotropy varies over the domain.
A {\em Voronoi refinement} algorithm generates triangulations in which no
triangle has an angle smaller than $20^\circ$, as measured from the skewed
perspective of any point in the triangle.

Joint work with Francois Labelle.

Host: Tamal Dey